Biometric feature extraction (also sometimes named minutia extraction) refers to the process by which established key features of a sample are selected or enhanced for more efficient processing. Typically, the process of feature extraction relies on a set of algorithms that varies depending on the type (face image or fingerprints, for example) of biometric identification used.

Biometric authentication is the matching of samples that have been converted (previously or upon attempt) from, for example, an image of a biometric trait into a searchable set of data.  This conversion is the process known as feature extraction.

If you look for example of how feature extraction fundamentally works, you see that it depends upon the type of sample, but is, for the most part, quite easy to conceptualize. You can head over to the following link to know more on how a biometric matching works: http://devtechnology.com/2013/11/emerging-biometric-technology-revocable-biometric-features/.